Spencer first rose to prominence in 2010 when he was selected by Gary Schofield for the BARLA (British Amateur Rugby League Association) under 19s tour of South Africa.
It was a successful trip for the side, and Spencer was snapped up by Wigan Warriors upon his return.
An experienced player, Spencer made his 100th career appearance in May of this year, before signing on a month’s loan with Oldham Roughyeds.
“I can’t wait to get to London,” he said.
“I’ve really enjoyed my time at Leigh and have a lot to thank the club for, but I’m looking forward to a different challenge now.
“I’ve watched London over the course of the season and you can tell they’re a tight knit group of lads who work hard for each other – not for individual success – and that’s really important in a club’s culture.
“I’m really excited about the move to the capital and joining the boys, and I can’t wait to see what 2017 brings!”
London head coach Andrew Henderson is pleased to have secured the talented front-rower.
“Tom will bring some size and power to the team. He has come through a very good Wigan system as a kid and went on to gain some Super League experience with the Warriors.
“As a youngster he spent time on dual registration with Leigh – where he impressed – before joining the Centurions full-time, so I have seen a lot of him over the past few seasons.
“I think he has been excellent in his time with Leigh, however this season his opportunities have been limited with the changes and number of players in the squad.
“At 25 he has his best years ahead of him and we look forward to bringing the best out of him.
“He has a lot of experience behind him at a young age, the right attitude and qualities that we look for in our players, which can only be a boost to our 2017 squad and beyond.”
Leigh Centurions owner Derek Beaumont said: “I am really pleased for Tom that he has secured this challenge and what will be a new life style for him.
“He is a 100% committed individual, and has been a great servant to this club doing everything to the best of his ability – always applying himself to every task.
“In the early years of my tenure Tom was on dual registration and was our main forward with a lot of responsibility, which he always carried well.
“I have no doubt whatsoever he will relish the challenge at London and be an excellent signing for them.
“He goes with our best wishes and he is another player who I have no doubt will remain committed here until the job is done and enjoy any success we may have between now and the end of the season.
“Tom was a crowd favourite and I am sure that will become the case at the Broncos.”